How do you simplify (7+2)^2 using order of operations?

1 Answer
Mar 15, 2016

See solution below.

Explanation:

The order of operations are:

1. Parentheses

2. Exponents

3. Multiplication/division (working from left to right)

4. Addition/subtraction (working from left to right)

The following poster gives you a little sentence to help you remember as you learn:

Or, quite simply, you can remember by using the commonly used acronym PEDMAS.

Now to your problem.

Since parentheses always takes priority over exponents, you must evaluate inside the parentheses before squaring the result of that calculation.

${\left(7 + 2\right)}^{2}$

$= {\left(9\right)}^{2}$

$= 81$

So, the answer is 81.

Practice exercises:

1. Evaluate the following expressions.

a) $2 + 5 \times {\left(\frac{6}{3}\right)}^{2}$

b) $\frac{\frac{6}{3} \times \left(4 + 9\right)}{2}$

Challenge problem:

A student tried unsuccessfully to evaluate ${\left(\frac{{6}^{2} + {4}^{2}}{4 \left({2}^{2} - 5\right)}\right)}^{2}$

Here are his proofs:

1. ${\left(\frac{{6}^{2} + {4}^{2}}{4 \left({2}^{2} - 5\right)}\right)}^{2}$

2 ${\left(\frac{36 + 16}{4 \left(4 - 5\right)}\right)}^{2}$

$3. {52}^{2} / \left({4}^{2} \times - {1}^{2}\right)$

$4. \frac{2704}{16}$

$5. 169$

Multiple choice:

In which step did he make his first error?

a) 2

b) 3

c) 4

d) 5

Answer with proofs:

Correct his answer.